Applied and Computational Control, Signals, and Circuits, Volume 1

Applied and Computational Control, Signals, and Circuits
Volume 1

by Biswa Nath Datta (Editor)
Published by Birkhauser, 1999
539 pages, $69

reviewed by
Dan Simon
Innovatia Software
dansimon@innovatia.com

This is the first in an annual series devoted to the timely dissemination of research results in controls, signals, and circuit theory. The series attempts to appeal to a wide audience by emphasizing the computational and applications aspects of academic theory. This first volume contains ten invited chapters.

The first chapter is titled “Discrete Event Systems: The State of the Art and New Directions.” It begins with a survey of the field for newcomers. The chapter continues with a discussion of Discrete Event System (DES) modeling and then reviews the current state of the art. The remainder of the chapter presents some open problems and suggested directions for research. These include decentralized DES control in order to overcome computational barriers, the application of DES to fault detection, methods for handling uncertainty in DES, and the integration of DES control with more traditional time-driven control systems. This chapter is a truly beneficial survey of the field. It would be most useful to a researcher who has already read an introductory book [e.g., 1] and wants to dig deeper in a structured way in order to develop a research program in the field.

The second chapter, “Array Algorithms for H-two and H-infinity Estimation,” deals primarily with the development of H-infinity filters using array algorithms (also called square root algorithms). This contribution includes a review of existing results but also contains new research that builds on the work of [2,3]. Square root algorithms were developed for Kalman filters in the late 1960s, and this chapter extends that work to H-infinity filtering. Square root algorithms are developed for the family of all H-infinity filters, and in particular for the central filter. This chapter reviews the computational savings that can be realized in the application of square root H-two filters if the system is time-invariant. The H-two results are then generalized to square root H-infinity filters for time-invariant systems.

Chapter 3, called “Nonuniqueness, Uncertainty, and Complexity in Modeling,” is based on a conference paper by the author [4]. This is an expository chapter that deals more with concepts than mathematics. It does not contain any new material but presents an overview of results from the 1990s. Because of the finiteness of data, the uncertainty of observation, and the complexity of the real world, the true model of a real system can never be exactly known. Traditional modeling methods attempt to remove the nonuniqueness of the problem, but this author claims that it is more natural to synthesize a model that intrinsically contains uncertainty. Thus the limitation of knowledge is retained in the model rather than being artificially suppressed. This leads to the notion of a model set, which ties in nicely with the field of robust control. This chapter is an interesting tutorial on a relatively new topic.

The fourth chapter is titled “Iterative Learning Control: An Expository Overview.” Iterative Learning Control (ILC), first introduced in 1978 [5], is a scheme that is applied to finite time systems that execute repetitively. A classic example is a robot involved in an assembly operation. ILC algorithms provide a way of improving the system performance from one process iteration to the next. This chapter is tutorial in nature and gives two simple examples to illustrate the use of ILC. The chapter contains an impressive collection of 254 references, neatly arranged by topic. Interesting connections are shown between ILC and other control paradigms (feedback control, optimal control, adaptive control, robust control, and intelligent control). The chapter concludes with a summary of six important areas for future ILC research.

The fifth chapter changes gears and presents some mathematically oriented results on the topic of “FIR Filter Design via Spectral Factorization and Convex Optimization.” The authors consider the classic finite impulse response (FIR) filter design problem with inequality constraints on the frequency response magnitude. This problem in turn gives rise to a nonconvex optimization problem. This makes it difficult to find a globally optimal solution. But the authors present a creative method using spectral factorization to transform the optimization problem into a nonlinear convex problem. As such, a globally optimal solution can be found. The method is illustrated on several examples, including lowpass filter design, equalizer design, and antenna array weight optimization.

Chapter 6 is titled “Algorithms for Subspace State-Space System Identification: An Overview.” Traditional system identification methods (i.e., prediction error methods) focus on models such as the autoregressive moving average model. But the 1990s witnessed the birth of state space identification [6], driven by the volume of control work that is done in the state space environment. This chapter presents an overview of the field of state space identification and compares this new field with the traditional prediction error methods. The authors present several nice comparisons between prediction error methods and state space methods, including comparisons of accuracy and computational effort. In general, prediction error methods are more accurate while state space methods are much quicker. The authors therefore do not view the two methods as competitive but rather as complementary. An initial model can be quickly identified with state space methods and then fine tuned (if needed) with the more accurate but slower prediction error methods. The state space identification methods are extended to periodic systems, bilinear systems, and closed loop systems. The authors discuss available state space identification software and include a number of web sites in their footnotes.

The seventh chapter is titled “Iterative Solution Methods for Large Linear Discrete Ill-Posed Problems.” The chapter is concerned with solving the equation Ax=b for the vector x, where A is a near-singular matrix, and b is corrupted by noise and hence may not be in the range of A. The vector x could contain on the order of a million elements. Some applications that give rise to this type of problem include image restoration, computer tomography, and electromagnetics. This problem frequently is ill posed, which means that the solution does not depend continuously on the data. So the problem can be modified by a process called regularization so that it is well posed. This chapter presents a survey of iterative solution methods for the given problem, and also suggests a new iterative algorithm that uses an exponential filter function. The authors present a number of algorithms in pseudo code and conclude their chapter with some examples of image restoration.

Chapter 8, titled “Wavelet-Based Image Coding: An Overview,” deals with image compression using wavelet technology. The authors present tutorial material on quantization, vector quantization (the extension of quantization to multiple dimensions), and transform coding (a computationally efficient alternative to vector quantization). The material on transform coding includes the Karhunen-Loeve transform, the discrete cosine transform, and subband transforms. An overview of wavelets follows, along with an explanation of how they can be used in transform coding. Several examples are given along with pointers to web sites that contain source code and additional data.

The ninth chapter is titled “Reduced-Order Modeling Techniques Based on Krylov Subspaces and Their Use in Circuit Simulation.” This chapter is motivated by the need to simulate circuits with millions of devices [7]. The direct simulation of such circuits is computationally infeasible. Instead such systems need to be reduced to a smaller order so that they can be more easily simulated. The order reduction discussed here relates to state space models. The author delves into the use of Krylov subspaces, Lanczos processes, and Arnoldi algorithms for order reduction. Examples are presented for systems with several thousand state variables that are reduced by as much as two orders of magnitude without much loss of transfer function information.

The tenth and final chapter, “SLICOT – A Subroutine Library in Systems and Control Theory,” describes a freeware library of control algorithms. SLICOT is an acronym for Subroutine Library in Control Theory, and is written in Fortran 77. It is maintained and developed by the Numerics in Control Network (NICONET), which is a project of the Working Group on Software (WGS). SLICOT is built on top of two well known libraries – the Basic Linear Algebra Subroutines (BLAS) and the Linear Algebra Package (LAPACK). The authors motivate the use of SLICOT by comparing it to MATLAB. There is a need for the availability of control theory routines in a portable low level language such as C or Fortran. In addition, MATLAB routines may be computationally inefficient because of its highly object oriented architecture. Finally, some of MATLAB’s routines are not as numerically robust as one might desire. The main emphasis in SLICOT is numerical robustness and efficiency. The authors present several examples of problems for which SLICOT executed much faster and somewhat more accurately than MATLAB. SLICOT has a long and somewhat convoluted history dating back to the early 1980s but it did not exist on its own until 1990. It is freely available from the internet and contains about 250 routines, most of which have associated example programs, data and results. New routines are continuously in preparation. SLICOT is a collaborative effort; the web site lists about 35 contributors to the routines. SLICOT routines should generally be considered as complementary to MATLAB as they can be linked to MATLAB through a gateway compiler. This chapter lists a number of web sites associated with SLICOT and provides a useful overview for anyone interested in using or contributing to this freeware.

Overall I highly recommend this book. The material is substantive, well researched, and written by leading experts. However, most readers will not be interested in the entire book but will rather be interested in only a chapter or two. This book could be used by individual researchers or as a text for an advanced control topics course.

References

[1] A. Tornambe, Discrete-Event System Theory: An Introduction. World Scientific Publishing Company, 1995.

[2] B. Hassibi, A. Sayed, and T. Kailath, “Linear estimation in Krein space – Part I: Theory,” IEEE Transactions on Automatic Control, vol. 41, no. 1, pp. 18-33, 1996.

[3] B. Hassibi, A. Sayed, and T. Kailath, “Linear estimation in Krein space – Part II: Applications,” IEEE Transactions on Automatic Control, vol. 41, no. 1, pp. 34-49, 1996.

[4] H. Kimura, “How does the model get reality?” Second Asian Control Conference, Seoul, pp. 3-10, 1996.

[5] M. Uchiyama, “Formation of high speed motion pattern of mechanical arm by trial,” Transactions of the Society of Instrumentation and Control Engineers, vol. 19, no. 5, pp. 706-712, 1978.

[6] Special Issue on Subspace Methods, Signal Processing, vol. 52, no. 2, 1996.

[7] J. Vlach and K. Singhal, Computer methods for circuit analysis and design. Van Nostrand Reinhold, 1993.

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Last Revised: March 13, 2001